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What is the largest rectangle that can be inscribed in the first quadrant of the ellipse 9x^2+16y^2=144?

  • Calculus -

    base along x-axis, height along y-axis, bottom left vertex at (0,0).
    let the top right vertex be (x,y)
    from equation
    y = (1/4)√(144 - 9x^2)

    Area = xy
    = x(1/4)√(144 - 9x^2)
    differentiate using the product rule, set the derivative equal to zero and solve for x
    I got x = 4√3/3 for a max area of 384√3/3

    but check my arithmetic.

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